TSTP Solution File: SEU062+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n004.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:31:52 EDT 2022

% Result   : Theorem 0.21s 0.52s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   41 (   8 unt;   0 def)
%            Number of atoms       :  121 (  27 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  135 (  55   ~;  35   |;  27   &)
%                                         (   5 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   67 (  56   !;  11   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f304,plain,
    $false,
    inference(subsumption_resolution,[],[f303,f184]) ).

fof(f184,plain,
    in(sK8(sK7,relation_rng(sK6)),sK7),
    inference(resolution,[],[f132,f124]) ).

fof(f124,plain,
    ~ subset(sK7,relation_rng(sK6)),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ( relation(sK6)
    & ! [X2] :
        ( empty_set != relation_inverse_image(sK6,singleton(X2))
        | ~ in(X2,sK7) )
    & ~ subset(sK7,relation_rng(sK6)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7])],[f60,f82]) ).

fof(f82,plain,
    ( ? [X0,X1] :
        ( relation(X0)
        & ! [X2] :
            ( empty_set != relation_inverse_image(X0,singleton(X2))
            | ~ in(X2,X1) )
        & ~ subset(X1,relation_rng(X0)) )
   => ( relation(sK6)
      & ! [X2] :
          ( empty_set != relation_inverse_image(sK6,singleton(X2))
          | ~ in(X2,sK7) )
      & ~ subset(sK7,relation_rng(sK6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f60,plain,
    ? [X0,X1] :
      ( relation(X0)
      & ! [X2] :
          ( empty_set != relation_inverse_image(X0,singleton(X2))
          | ~ in(X2,X1) )
      & ~ subset(X1,relation_rng(X0)) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ? [X0,X1] :
      ( ~ subset(X1,relation_rng(X0))
      & ! [X2] :
          ( empty_set != relation_inverse_image(X0,singleton(X2))
          | ~ in(X2,X1) )
      & relation(X0) ),
    inference(ennf_transformation,[],[f39]) ).

fof(f39,plain,
    ~ ! [X0,X1] :
        ( relation(X0)
       => ( ! [X2] :
              ~ ( in(X2,X1)
                & empty_set = relation_inverse_image(X0,singleton(X2)) )
         => subset(X1,relation_rng(X0)) ) ),
    inference(rectify,[],[f27]) ).

fof(f27,negated_conjecture,
    ~ ! [X1,X0] :
        ( relation(X1)
       => ( ! [X2] :
              ~ ( in(X2,X0)
                & empty_set = relation_inverse_image(X1,singleton(X2)) )
         => subset(X0,relation_rng(X1)) ) ),
    inference(negated_conjecture,[],[f26]) ).

fof(f26,conjecture,
    ! [X1,X0] :
      ( relation(X1)
     => ( ! [X2] :
            ~ ( in(X2,X0)
              & empty_set = relation_inverse_image(X1,singleton(X2)) )
       => subset(X0,relation_rng(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_funct_1) ).

fof(f132,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | in(sK8(X0,X1),X0) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( in(sK8(X0,X1),X0)
          & ~ in(sK8(X0,X1),X1) ) )
      & ( ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f86,f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( in(X2,X0)
          & ~ in(X2,X1) )
     => ( in(sK8(X0,X1),X0)
        & ~ in(sK8(X0,X1),X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) ) )
      & ( ! [X3] :
            ( ~ in(X3,X0)
            | in(X3,X1) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( in(X2,X0)
            & ~ in(X2,X1) ) )
      & ( ! [X2] :
            ( ~ in(X2,X0)
            | in(X2,X1) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( ~ in(X2,X0)
          | in(X2,X1) ) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( in(X2,X0)
         => in(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

fof(f303,plain,
    ~ in(sK8(sK7,relation_rng(sK6)),sK7),
    inference(trivial_inequality_removal,[],[f300]) ).

fof(f300,plain,
    ( ~ in(sK8(sK7,relation_rng(sK6)),sK7)
    | sK13 != sK13 ),
    inference(superposition,[],[f165,f285]) ).

fof(f285,plain,
    relation_inverse_image(sK6,singleton(sK8(sK7,relation_rng(sK6)))) = sK13,
    inference(resolution,[],[f206,f124]) ).

fof(f206,plain,
    ! [X4] :
      ( subset(X4,relation_rng(sK6))
      | relation_inverse_image(sK6,singleton(sK8(X4,relation_rng(sK6)))) = sK13 ),
    inference(resolution,[],[f200,f131]) ).

fof(f131,plain,
    ! [X0,X1] :
      ( ~ in(sK8(X0,X1),X1)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f200,plain,
    ! [X5] :
      ( in(X5,relation_rng(sK6))
      | relation_inverse_image(sK6,singleton(X5)) = sK13 ),
    inference(resolution,[],[f163,f126]) ).

fof(f126,plain,
    relation(sK6),
    inference(cnf_transformation,[],[f83]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ~ relation(X1)
      | relation_inverse_image(X1,singleton(X0)) = sK13
      | in(X0,relation_rng(X1)) ),
    inference(backward_demodulation,[],[f140,f160]) ).

fof(f160,plain,
    empty_set = sK13,
    inference(resolution,[],[f159,f152]) ).

fof(f152,plain,
    empty(sK13),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ( empty(sK13)
    & relation(sK13) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f15,f104]) ).

fof(f104,plain,
    ( ? [X0] :
        ( empty(X0)
        & relation(X0) )
   => ( empty(sK13)
      & relation(sK13) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,axiom,
    ? [X0] :
      ( empty(X0)
      & relation(X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).

fof(f159,plain,
    ! [X0] :
      ( ~ empty(X0)
      | empty_set = X0 ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(f140,plain,
    ! [X0,X1] :
      ( ~ relation(X1)
      | empty_set = relation_inverse_image(X1,singleton(X0))
      | in(X0,relation_rng(X1)) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1] :
      ( ( ( empty_set != relation_inverse_image(X1,singleton(X0))
          | ~ in(X0,relation_rng(X1)) )
        & ( in(X0,relation_rng(X1))
          | empty_set = relation_inverse_image(X1,singleton(X0)) ) )
      | ~ relation(X1) ),
    inference(rectify,[],[f95]) ).

fof(f95,plain,
    ! [X1,X0] :
      ( ( ( empty_set != relation_inverse_image(X0,singleton(X1))
          | ~ in(X1,relation_rng(X0)) )
        & ( in(X1,relation_rng(X0))
          | empty_set = relation_inverse_image(X0,singleton(X1)) ) )
      | ~ relation(X0) ),
    inference(nnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X1,X0] :
      ( ( empty_set != relation_inverse_image(X0,singleton(X1))
      <=> in(X1,relation_rng(X0)) )
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f38]) ).

fof(f38,plain,
    ! [X1,X0] :
      ( relation(X0)
     => ( empty_set != relation_inverse_image(X0,singleton(X1))
      <=> in(X1,relation_rng(X0)) ) ),
    inference(rectify,[],[f25]) ).

fof(f25,axiom,
    ! [X1,X0] :
      ( relation(X1)
     => ( empty_set != relation_inverse_image(X1,singleton(X0))
      <=> in(X0,relation_rng(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t142_funct_1) ).

fof(f165,plain,
    ! [X2] :
      ( relation_inverse_image(sK6,singleton(X2)) != sK13
      | ~ in(X2,sK7) ),
    inference(backward_demodulation,[],[f125,f160]) ).

fof(f125,plain,
    ! [X2] :
      ( empty_set != relation_inverse_image(sK6,singleton(X2))
      | ~ in(X2,sK7) ),
    inference(cnf_transformation,[],[f83]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SEU062+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35  % Computer : n004.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Tue Aug 30 14:32:35 EDT 2022
% 0.14/0.35  % CPUTime    : 
% 0.21/0.50  % (1021)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.21/0.50  % (1010)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.21/0.50  % (999)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.21/0.51  % (996)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.51  % (995)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.51  % (1005)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.51  % (1002)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.51  % (1021)First to succeed.
% 0.21/0.52  % (1026)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.21/0.52  % (1010)Also succeeded, but the first one will report.
% 0.21/0.52  % (1021)Refutation found. Thanks to Tanya!
% 0.21/0.52  % SZS status Theorem for theBenchmark
% 0.21/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.52  % (1021)------------------------------
% 0.21/0.52  % (1021)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52  % (1021)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52  % (1021)Termination reason: Refutation
% 0.21/0.52  
% 0.21/0.52  % (1021)Memory used [KB]: 5628
% 0.21/0.52  % (1021)Time elapsed: 0.070 s
% 0.21/0.52  % (1021)Instructions burned: 8 (million)
% 0.21/0.52  % (1021)------------------------------
% 0.21/0.52  % (1021)------------------------------
% 0.21/0.52  % (989)Success in time 0.163 s
%------------------------------------------------------------------------------